PCI 6th Edition

1
PCI 6th Edition

• Flexural Component Design

2
Presentation Outline

• Whats new to ACI 318
• Gravity Loads
• Load Effects
• Concrete Stress Distribution
• Nominal Flexural Strength
• Flexural Strength Reduction Factors
• Shear Strength
• Torsion
• Serviceability Requirements

3
New to ACI 318 02

• Load Combinations
• Stress limits
• Member Classification
• Strength Reduction factor is a function of
  reinforcement strain
• Minimum shear reinforcement requirements
• Torsion Design Method

4
Load Combinations

• U 1.4 (D F)
• U 1.2 (D F T) 1.6 (L H) 0.5 (Lr or S
  or R)
• U 1.2D 1.6 (Lr or S or R) (1.0L or 0.8W)
• U 1.2D 1.6W 1.0L 0.5(Lr or S or R)
• U 1.2D 1.0E 1.0L 0.2S
• U 0.9D 1.6W 1.6H
• U 0.9D 1.0E 1.6H

5
Comparison of Load Combinations

• U1.2D 1.6 L 2002
• U 1.4D 1.7L 1999
• If L.75D
• i.e. a 10 reduction in required strength

6
Classifications

• No Bottom Tensile Stress Limits
• Classify Members Strength Reduction Factor
• Tension-Controlled
• Transition
• Compression Controlled
• Three Tensile Stress Classifications
• Class U Un-cracked
• Class T Transition
• Class C Cracked

7

• Copied from ACI 318 2002, ACI 318-02 table R18.3.3

8
Class C Members

• Stress Analysis Based on Cracked Section
  Properties
• No Compression Stress limit
• No Tension Stress limit
• Increase awareness on serviceability
• Crack Control
• Displacements
• Side Skin Reinforcement

9
Minimum Shear Reinforcing
1999
2002
10
System Loads

• Gravity Load Systems
• Beams
• Columns
• Floor Member Double Tees, Hollow Core
• Spandrels
• Tributary Area
• Floor members, actual top area
• Beams and spandrels
• Load distribution
• Load path
• Floor members ? spandrels or beams ? Columns

11
Live Load Reduction

• Live Loads can be reduced based on
• Where
• KLL 1
• Lo Unreduced live load and
• At tributary area

12
Live Load Reduction

• Or the alternative floor reduction shall not
  exceed
• or
• Where
• R reduction 40
• r .08

13
Member Shear and Moment

• Shear and moments on members can be found using
  statics methods and beam tables from Chapter 11

14
Strength Design

• Strength design is based using the rectangular
  stress block
• The stress in the prestressing steel at nominal
  strength, fps, can be determined by strain
  compatibility or by an approximate empirical
  equation
• For elements with compression reinforcement, the
  nominal strength can be calculated by assuming
  that the compression reinforcement yields. Then
  verified.
• The designer will normally choose a section and
  reinforcement and then determine if it meets the
  basic design strength requirement

15
Concrete Stress Distribution

• Parabolic distribution
• Equivalent rectangular distribution

16
Stress Block Theory

• Stress-Strain relationship
• is not constant

fc6,000 psi
fc3,000 psi
17
Stress Block Theory

• Stress-Strain relationship
• Stress-strain can be modeled by

Where strain at max.
stress
and max stress
18
Stress Block Theory

• The Whitney stress block is a simplified stress
  distribution that shares the same centroid and
  total force as the real stress distribution

19
Equivalent Stress Block b1 Definition

• b1 0.85
• when fc lt 3,000 psi
• b1 0.65
• when fc gt 8,000 psi

20
Design Strength

• Mild Reinforcement Non - Prestressed
• Prestress Reinforcement

21
Strength Design Flowchart

• Figure 4.2.1.2 page 4-9
• Non-Prestressed Path
• Prestressed Path

22
Non-Prestressed Members

• Find depth of compression block

23
Depth of Compression Block

• Where
• As is the area of tension steel
• As is the area of compression steel
• fy is the mild steel yield strength

Assumes compression steel yields
24
Flanged Sections

• Checked to verify that the compression block is
  truly rectangular

25
Compression Block Area

• If compression block is rectangular, the flanged
  section can be designed as a rectangular beam

26
Compression Block Area

• If the compression block is not rectangular (agt
  hf),

To find a
27
Determine Neutral Axis

• From statics and strain compatibility

28
Check Compression Steel

• Verify that compression steel has reached yield
  using strain compatibility

29
Compression Comments

• By strain compatibility, compression steel yields
  if
• If compression steel has not yielded, calculation
  for a must be revised by substituting actual
  stress for yield stress
• Non prestressed members should always be tension
  controlled, therefore c / dt lt 0.375
• Add compression reinforcement to create tesnion
  controlled secions

30
Moment Capacity

• 2 equations
• rectangular stress block in the flange section
• rectangular stress block in flange and stem
  section

31
Strength Design Flowchart
Figure 4.2.1.2page 4-9 Non- Prestressed
Path Prestressed Path
32
(No Transcript)
33
Stress in Strand

• fse - stress in the strand after losses
• fpu - is the ultimate strength of the strand
• fps - stress in the strand at nominal strength

34
Stress in Strand

• Typically the jacking force is 65 or greater
• The short term losses at midspan are about 10 or
  less
• The long term losses at midspan are about 20 or
  less

35
Stress in Strand

• Nearly all prestressed concrete is bonded

36
Stress in Strand

• Prestressed Bonded reinforcement
• gp factor for type of prestressing strand, see
  ACI 18.0
• .55 for fpy/fpu not less than .80
• .45 for fpy/fpu not less than .85
• .28 for fpy/fpu not less than .90 (Low
  Relaxation Strand)
• rp prestressing reinforcement ratio

37
Determine Compression Block
38
Compression Block Height

• Where
• Aps - area of prestressing steel
• fps - prestressing steel strength

39
Flange Sections Check
40
Compression Steel Check

• Verify that compression steel has reached yield
  using strain compatibility

41
Moment Capacity

• 2 Equations
• rectangular stress block in flange section
• rectangular stress block in flange and stem
  section

42
Flexural Strength Reduction Factor

• Based on primary reinforcement strain
• Strain is an indication of failure mechanism
• Three Regions

43
Member Classification

• On figure 4.2.1.2

44
Compression Controlled

• e lt 0.002 at extreme steel tension fiber or
• c/dt gt 0.600
• 0.70 with spiral ties
• 0.65 with stirrups

45
Tension Controlled

• e gt 0.005 at extreme steel tension fiber, or
• c/dt lt 0.375
• f 0.90 with spiral ties or stirrups

46
Transition Zone

• 0.002 lt e lt 0.005 at extreme steel tension fiber,
  or
• 0.375 lt c/dt lt 0.6
• f 0.57 67(e) or
• f 0.48 83(e) with spiral ties
• f 0.37 0.20/(c/dt) or
• f 0.23 0.25/(c/dt) with stirrups

47
Strand Slip Regions

• ACI Section 9.3.2.7
• where the strand embedment length is less than
  the development length
• f 0.75

48
Limits of Reinforcement

• To prevent failure immediately upon cracking,
  Minimum As is determined by
• As,min is allowed to be waived if tensile
  reinforcement is 1/3 greater than required by
  analysis

49
Limits of Reinforcement

• The flexural member must also have adequate
  reinforcement to resist the cracking moment
• Where

Correction for initial stresses on non-composite,
prior to topping placement
Section after composite has been applied,
including prestress forces
50
Critical Sections
51
Horizontal Shear

• ACI requires that the interface between the
  composite and non-composite, be intentionally
  roughened, clean and free of laitance
• Experience and tests have shown that normal
  methods used for finishing precast components
  qualifies as intentionally roughened

52
Horizontal Shear, Fh Positive Moment Region

• Based on the force transferred in topping (page
  4-53)

53
Horizontal Shear, Fh Negative Moment Region

• Based on the force transferred in topping (page
  4-53)

54
Unreinforced Horizontal Shear

• Where
• f 0.75
• bv width of shear area
• lvh - length of the member subject to shear,
  1/2 the span for simply supported members

55
Reinforced Horizontal Shear

• Where
• f 0.75
• rv - shear reinforcement ratio
• Acs - Area of shear reinforcement
• me - Effective shear friction coefficient

56
Shear Friction Coefficient
57
Shear Resistance by Non-Prestressed Concrete

• Shear strength for non-prestressed sections

58
Prestress Concrete Shear Capacity

• Where
• ACI Eq 11-9
• Effective prestress must be 0.4fpu
• Accounts for shear combined with moment
• May be used unless more detail is required

59
Prestress Concrete Shear Capacity

• Concrete shear strength is minimum is
• Maximum allowed shear resistance from concrete
  is

60
Shear Capacity, Prestressed

• Resistance by concrete when diagonal cracking is
  a result of combined shear and moment

Where Vi and Mmax - factored externally
applied loads e.g. no self weight Vd - is
un-factored dead load shear
61
Shear Capacity, Prestressed

• Resistance by concrete when diagonal cracking is
  a result of principal tensile stress in the web
  is in excess of cracking stress.

Where Vp the vertical component of
effective prestress force (harped or draped
strand only)
62
Vcmax

• Shear capacity is the minimum of Vc, or if a
  detailed analysis is used the minimum of Vci or
  Vcw

63
Shear Steel

• If
• Then

64
Shear Steel Minimum Requirements

• Non-prestressed members
• Prestressed members

Remember both legs of a stirrup count for Av
65
Torsion

• Current ACI
• Based on compact sections
• Greater degree of fixity than PC can provide
• Provision for alternate solution
• Zia, Paul and Hsu, T.C., Design for Torsion and
  Shear in Prestressed Concrete, Preprint 3424,
  American Society of Civil Engineers, October,
  1978. Reprinted in revised form in PCI JOURNAL,
  V. 49, No. 3, May-June 2004.

66
Torsion

• For members loaded two sides, such as inverted
  tee beams, find the worst case condition with
  full load on one side, and dead load on the other

67
Torsion

• In order to neglect Torsion
• Where
• Tu(min) minimum torsional strength provided by
  concrete

68
Minimum Torsional Strength

• Where
• x and y - are short and long side, respectively
  of a component rectangle
• g - is the prestress factor

69
Prestress Factor, g

• For Prestressed Members
• Where
• fpc level of prestress after losses

70
Maximum Torsional Strength

• Avoid compression failures due to over
  reinforcing
• Where

71
Maximum Shear Strength

• Avoid compression failures due to over reinforcing

72
Torsion/Shear Relationship

• Determine the torsion carried by the concrete
• Where
• Tc and Vc - concrete resistance under pure
  torsion and shear respectively
• Tc and Vc - portions of the concrete
  resistance of torsion and shear

73
Torsion/Shear Relationship

• Determine the shear carried by the concrete

74
Torsion Steel Design

• Provide stirrups for torsion moment - in addition
  to shear
• Where
• x and y - short and long dimensions of the
  closed stirrup

75
Torsion Steel Design

• Minimum area of closed stirrups is limited by

76
Longitudinal Torsion Steel

• Provide longitudinal steel for torsion based on
  equation
• or
• Whichever greater

77
Longitudinal Steel limits

• The factor in
• the second equation need not exceed

78
Detailing Requirements, Stirrups

• 135 degree hooks are required unless sufficient
  cover is supplied
• The 135 degree stirrup hooks are to be anchored
  around a longitudinal bar
• Torsion steel is in addition to shear steel

79
Detailing Requirements, Longitudinal Steel

• Placement of the bars should be around the
  perimeter
• Spacing should spaced at no more than 12 inches
• Longitudinal torsion steel must be in addition to
  required flexural steel (note at ends flexural
  demand reduces)
• Prestressing strand is permitted (_at_ 60ksi)
• The critical section is at the end of simply
  supported members, therefore U-bars may be
  required to meet bar development requirements

80
Serviceability Requirements

• Three classifications for prestressed components
• Class U Uncracked
• Class T Transition
• Class C Cracked

Stress
81
Uncracked Section

• Table 4.2.2.1 (Page 4.24)
• Easiest computation
• Use traditional mechanics of materials methods to
  determine stresses, gross section and deflection.
• No crack control or side skin reinforcement
  requirements

82
Transition Section

• Table 4.2.2.1 (Page 4.24)
• Use traditional mechanics of materials methods to
  determine stresses only.
• Use bilinear cracked section to determine
  deflection
• No crack control or side skin reinforcement
  requirements

83
Cracked Section

• Table 4.2.2.1 (Page 4.24)
• Iterative process
• Use bilinear cracked section to determine
  deflection and to determine member stresses
• Must use crack control steel per ACI 10.6.4
  modified by ACI 18.4.4.1 and ACI 10.6.7

84
Cracked Section Stress Calculation

• Class C member require stress to be check using a
  Cracked Transformed Section
• The reinforcement spacing requirements must be
  adhered to

85
Cracked Transformed Section Property Calculation
Steps

• Step 1 Determine if section is cracked
• Step 2 Estimate Decompression Force in Strand
• Step 3 Estimate Decompression Force in mild
  reinforcement (if any)
• Step 4 Create an equivalent force in topping if
  present
• Step 5 Calculate transformed section of all
  elements and modular ratios
• Step 6 Iterate the location of the neutral axis
  until the normal stress at this level is zero
• Step 7 Check Results with a a moment and force
  equilibrium set of equations

86
Steel Stress

• fdc decompression stress
• stress in the strand when the surrounding
  concrete stress is zero Conservative to use,
  fse (stress after losses) when no additional mild
  steel is present.

87
Simple Example

• Page 4-31

88
(No Transcript)
89
(No Transcript)
90
(No Transcript)
91
(No Transcript)
92
Deflection Calculation Bilinear Cracked Section

• Deflection before the member has cracked is
  calculated using the gross (uncracked) moment of
  inertia, Ig
• Additional deflection after cracking is
  calculated using the moment of inertia of the
  cracked section Icr

93
Effective Moment of Inertia

• Alternative method

Where ftl final stress fl stress due
to live load fr modulus of rupture
94
Prestress Losses

• Prestressing losses
• Sources of total prestress loss (TL)
• TL ES CR SH RE
• Elastic Shortening (SH)
• Creep (CR)
• Shrinkage (SH)
• Relaxation of tendons (RE)

95
Elastic Shortening

• Caused by the prestressed force in the precast
  member
• Where
• Kes 1.0 for pre-tensioned members
• Eps modulus of elasticity of prestressing
  tendons (about 28,500 ksi)
• Eci modulus of elasticity of concrete at time
  prestress is applied
• fcir net compressive stress in concrete at
  center of gravity of prestressing force
  immediately after the prestress has been applied
  to the concrete

96
fcir

• Where
• Pi initial prestress force (after anchorage
  seating loss)
• e eccentricity of center of gravity of tendons
  with respect to center of gravity of concrete at
  the cross section considered
• Mg bending moment due to dead weight of
  prestressed member and any other permanent loads
  in place at time of prestressing
• Kcir 0.9 for pretensioned members

97
Creep

• Creep (CR)
• Caused by stress in the concrete
• Where
• Kcr 2.0 normal weight concrete
• 1.6 sand-lightweight concrete
• fcds stress in concrete at center of gravity
  of prestressing force due to all uperimposed
  permanent dead loads that are applied to the
  member after it has been prestressed

98
fcds

• Where
• Msd moment due to all superimposed permanent
  dead and sustained loads applied after
  prestressing

99
Shrinkage

• Volume change determined by section and
  environment
• Where
• Ksh 1.0 for pretensioned members
• V/S volume-to-surface ratio
• R.H. average ambient relative humidity from
  map

100
Relative Humidity

• Page 3-114 Figure 3.10.12

101
Relaxation

• Relaxation of prestressing tendons is based on
  the strand properties
• Where
• Kre and J - Tabulated in the PCI handbook
• C - Tabulated or by empirical equations in the
  PCI handbook

102
Relaxation Table

• Values for Kre and J for given strand
• Table 4.7.3.1 page 4-85

103
Relaxation Table Values for C

• fpi initial stress in prestress strand
• fpu ultimate stress for prestress strand
• Table 4.7.3.2 (Page 4-86)

104
Prestress Transfer Length

• Transfer length Length when the stress in the
  strand is applied to the concrete
• Transfer length is not used to calculate capacity

105
Prestress Development Length

• Development length - length required to develop
  ultimate strand capacity
• Development length is not used to calculate
  stresses in the member

106
Beam Ledge Geometry
107
Beam Ledge Design

• For Concentrated loads where s gt bt hl, find
  the lesser of

108
Beam Ledge Design

• For Concentrated loads where s lt bt hl, find
  the lesser of

109
Beam Ledge Reinforcement

• For continuous loads or closely spaced
  concentrated loads
• Ledge reinforcement should be provided by 3
  checks
• As, cantilevered bending of ledge
• Al, longitudinal bending of ledge
• Ash, shear of ledge

110
Beam Ledge Reinforcement

• Transverse (cantilever) bending reinforcement, As
• Uniformly spaced over width of 6hl on either side
  of the bearing

• Not to exceed half the distance to the next load
• Bar spacing should not exceed the ledge depth,
  hl, or 18 in

111
Longitudinal Ledge Reinforcement

• Placed in both the top and bottom of the ledge
  portion of the beam
• Where
• dl - is the depth of steel
• U-bars or hooked bars may
• be required to develop
• reinforcement at the end
• of the ledge

112
Hanger Reinforcement

• Required for attachment of the ledge to the web

• Distribution and spacing of Ash reinforcement
  should follow the same guidelines as for As

113
Hanger (Shear) Ledge Reinforcement

• Ash is not additive to shear and torsion
  reinforcement
• m is a modification factor which can be
  derived, and is dependent on beam section
  geometry. PCI 6th edition has design aids on
  table 4.5.4.1

114
Dap Design

• (1) Flexure (cantilever bending) and axial
  tension in the extended end. Provide flexural
  reinforcement, Af, plus axial tension
  reinforcement, An.

115
Dap Design

• (2) Direct shear at the junction of the dap and
  the main body of the member. Provide shear
  friction steel, composed of Avf Ah, plus axial
  tension reinforcement, An

116
Dap Design

• (3) Diagonal tension emanating from the
  re-entrant corner. Provide shear reinforcement,
  Ash

117
Dap Design

• (4) Diagonal tension in the extended end. Provide
  shear reinforcement composed of Ah and Av

118
Dap Design

• (5) Diagonal tension in the undapped portion.
  This is resisted by providing a full development
  length for As beyond the potential crack.

119
Dap Reinforcement

• 5 Main Areas of Steel
• Tension - As
• Shear steel - Ah

• Diagonal cracking Ash, Ash
• Dap Shear Steel - Av

120
Tension Steel As

• The horizontal reinforcement is determined in a
  manner similar to that for column corbels

121
Shear Steel Ah

• The potential vertical crack (2) is resisted by a
  combination of As and Ah

122
Shear Steel Ah

• Note the development ld of Ah beyond the assumed
  crack plane. Ah is usually a U-bar such that the
  bar is developed in the dap

123
Diagonal Cracking Steel Ash

• The reinforcement required to resist diagonal
  tension cracking starting from the re-entrant
  corner (3) can be calculated from

124
Dap Shear Steel Av

• Additional reinforcement for Crack (4) is
  required in the extended end, such that

125
Dap Shear Steel Av

• At least one-half of the reinforcement required
  in this area should be placed vertically. Thus

126
Dap Limitations and Considerations

• Design Condition as a dap if any of the following
  apply
• The depth of the recess exceeds 0.2H or 8 in.
• The width of the recess (lp) exceeds 12 in.
• For members less than 8 in. wide, less than
  one-half of the main flexural reinforcement
  extends to the end of the member above the dap
• For members 8 in. or more wide, less than
  one-third of the main flexural reinforcement
  extends to the end of the member above the dap

127
Questions?